Quadratic spherical spline quasi-interpolants on Powell–Sabin partitions

Spline quasi-interpolation methods are local tools approximating functions or discrete data. In this paper we deal with the problem of constructing quasi-interpolants in the space of quadratic spherical Powell–Sabin splines on uniform spherical triangulations of a sphere-like surface S. Discrete and differential quasi-interpolants of optimal approximation order are developed and numerical tests for illustrating theoretical results are presented.